5. Test the exactness of ODE, if not, use an integrating factor to make exact and then find general solution: (3x'y' + 2xy)dx +(2x'y' - x*) dy = ( =0.

Q: Use the method of reduction of order to find a second solution of the differential equation xy" – y'…

A: We are given the differential equation xy''-y'+4x3y=0, x>0 and one solution as y1(x)=sinx3. Now,…

Q: Is differential equation (4xy + 3y4)dx + (2x² + 5xy³)dy = 0 exact? If it is not exact what is its…

A: Given differential equation 4xy+3y4dx+2x2+5xy3dy=0. Is the differential equation exact? If not find…

Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

A: y=Ae5x+Be6x

Q: Verify that the function y = 6x − 4 sin x + 1 is a particular solution of the differential equation…

A:

Q: Find the differential dy of the given function.     y = 3x2/3

A:

Q: The differential equation obtained by eliminating the arbitrary constants A and B from the relation…

A: Please see the answer in step 2

Q: 5) If f is an everywhere differentiable function, show that 2. flxiy) = X-Y satisfies the partial…

A:

Q: find a linear differential operator that annihilates the given function. y = x sin(3x)+ 3xe6x

A:

Q: What is the differential equation of the orthogonal trajectories of х3 — Зху — у3 — с? (1) (x +…

A:

Q: Provided the integrating factor (IF) = xy2, find the general soution of the differential equation…

A: Multiply the integrating factor in the differential equation to make it exact.

Q: 7. Find the solution of the differential equation using Laplace Transform. y" – 3y' + 2y = e3x when…

A: We need to solve DE.

Q: Solve for the particular solution of the following differential equUations. a. (x³ + 3y)dx –- xdy;…

A: The given differential equation is: x3+3ydx-x dy=0 ;    y(1)=3

Q: Evaluate the general Solution to the differential equation: Cy-cos-x)dx+ cosxody A y(secx + tan x) t…

A:

Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A +…

A: Here we find the first order differential equation of given function.

Q: Find the differential dy of the given function. y = 3x2 − 4

A: Given function is Differentiating with respect to x, we get Therefore , differential dy is

Q: 3. Write the exact differential: f(x,y)=e-y-el-

A: Given- fx,y=ex-y-ey-x To write the exact differential.

Q: If df = y(xy + 1)dx - xdy, determine if is a state function of the variables x and y, if not, what…

A: Here we have to check that df is exact or not

Q: y(x²y² – 1)dx + x(x²y² + 1)dy = 0

A:

Q: х+1 y = 2x

A:

Q: 5. Verify that y(x) = Vx+C is a solution of the differential dy dx 1 for every constant C. equation…

A: The differential equation is given as dydx=12y2ydy=1dx

Q: Find the differential dy of the given function. y = (x + 1)/(2x − 1)

A:

Q: 6) Solve the homogeneous differential x2 + y? dy quation dx 2xy

A: on solving this we get

Q: Find the general solution to the differential equatio y" + 4y = cos 2x (where y' = ) dx

A: When the right-hand side of a higher-order linear differential equation contains a function of the…

Q: () 2. If k = w3 – wv², w=xy, v = w+ x, find and using: dw a) the chain rule b) differentials.

A: Given: k=w3-wv2, w=xy, v=w+x   To find: (∂k∂w)x . (∂k∂x)w  using chain rule and differentials

Q: (t + z cos(t)) dt + (sin(t) – 3z2 + 5) dz = 0

A:

Q: Show that the function y =  A e-x    + B x e-x satisfies the differentialequation y"   +2y' + y  =0

A: The given differential equation is y''+2y'+y=0. Let y=Ae-x+Bxe-x. This implies that,…

Q: find the integrating factor of the given linear DE and general solution of the y'+1/x (y)=cos(x)

A: Consider the given linear differential equation. y'+1xy=cosx The objective of the problem is to find…

Q: 7. Find the differential dy for y = x2 – 4x + 6, then evaluate it when x = 2 and dx = 0.1 -

A:

Q: For which value of k is the differential equation (x^k+y^k)dx + (2xy)dy = 0 becomes homogeneous?

A:

Q: Verify that the indicated expression is an implicit solution of the given differential equation. 1 (…

A:

Q: Show that y = x+vx +1 satisfies the differential equation (x + 1)°Y + x°Y. ydy -m³y 0 + X- dx2 dx

A:

Q: х+1 y 2x 1

A: Given,            y = x + 12x - 1

Q: 5. Test the exactness of ODE, if not, use an integrating factor to make exact and then find general…

A:

Q: 5. z = yex+x Iny xey-y lnx

A:

Q: Obtain the differential equation of the family of straight lines with slope and y-intercept equal.…

A: Differential equations

Q: Solve the differential equation (21xy + 21y²) + (7x² +21xy) y = 0 using the integrating factor u(x,…

A: Given : A differential equation (21xy+21y2)+(7x2+21xy)y'=0. The integrating factor is…

Q: 8. Compute the differential df of f(x,y) = log (x² + y²).

A: Given; f(x,y) = log(x2+ y2)

Q: Consider P(D)y = 0. What conditions on the rootsof the auxiliary equation would guarantee that…

A: Solution: Consider the given Differential Equation P(D)y = 0 Let the Auxiliary Equation of given DE…

Q: Is the function p(x, y) = sin? (xy²) a solution to the partial differential equation + (2x + y)(2y)…

A: Use 2sinxcosx=sin2x And put the given solution on both sides we get both sides are equal  And…

Q: 1 Verify that + xe3x 3 -3x e dx is the particular integral to the differential equation | dy 1 + 9y…

A: Variation of parameters, also known as variation of constants, is a general method to solve…

Q: 1 Solve for the differential of y when y=sinzx, x=÷, and dx= - 3 A) B) 2 -- C) D)

A:

Q: 4. Given that x=0 when y = 8, show that the general solution of the differential dy equation (x +4)…

A:

Q: Find the function y: (0.x) → R that satisfies the ordinary differential equation ry'(x) + y(x) = x²…

A: Given : y : 0 , ∞→ℝ   ;  xy'(x)+y(x)=x2 cosx        ;  yπ = 0 To Find : solution of ordinary…

Q: 1. Given y = 4e* + In x, find the differential dy.

A: See the attachment

Q: Consider the following differential equation. (x2 + y2)y′ = y2 Let  f(x, y) =  y2/x2 + y2 .  Find…

A: This is a problem of differentiation of the function. Based on the general formula we will answer…

Q: Consider the differential equation y = x+ y. Use Euler's method with Ax = 0.1 to estimate y when x =…

A: Let fx,y=x+y. Substitute 0 for n, 0.1 for h, -1 for x0 and 0 for y0 in the Euler's formula…

Q: Find the differential dy of the given function.    y = x√(1 − x2)

A:

Q: Find the value of the differential dy for y = e3x + 5x if x = 0 and dx = 0.1.

A: We know the differential dy of  y=f(x) is given by, dy=f'(x) dx

Q: 4. Find an integrating factor that is a function of only one variable, and find an implicit…

A: on solving this differential equation istly we will make this exact differential equation on finding…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.